msinit

Function: msinit
Section: modular_symbols
C-Name: msinit
Prototype: GGD0,L,
Help: msinit(G, V, {sign=0}): given G a finite index subgroup of SL(2,Z)
 and a finite dimensional representation V of GL(2,Q), creates a space of
 modular symbols, the G-module Hom_G(Div^0(P^1 Q), V). This is canonically
 isomorphic to H^1_c(X(G), V), and allows to compute modular forms for G.
 If sign is present and nonzero, it must be +1 or -1 and we consider
 the subspace defined by Ker (Sigma - sign), where Sigma is induced by
 [-1,0;0,1]. Currently the only supported groups are the Gamma_0(N), coded by
 the integer N. The only supported representation is V_k = Q[X,Y]_{k-2}, coded
 by the integer k >= 2.
Doc: given $G$ a finite index subgroup of $\text{SL}(2,\Z)$
 and a finite dimensional representation $V$ of $\text{GL}(2,\Q)$, creates a
 space of modular symbols, the $G$-module $\Hom_G(\text{Div}^0(\P^1
 (\Q)), V)$. This is canonically isomorphic to $H^1_c(X(G), V)$, and allows to
 compute modular forms for $G$. If \emph{sign} is present and nonzero, it
 must be $\pm1$ and we consider the subspace defined by $\text{Ker} (\sigma -
 \var{sign})$, where $\sigma$ is induced by \kbd{[-1,0;0,1]}. Currently the
 only supported groups are the $\Gamma_0(N)$, coded by the integer $N > 0$.
 The only supported representation is $V_k = \Q[X,Y]_{k-2}$, coded by the
 integer $k \geq 2$.
 \bprog
 ? M = msinit(11,2); msdim(M) \\ Gamma0(11), weight 2
 %1 = 3
 ? mshecke(M,2) \\ T_2 acting on M
 %2 =
 [3  1  1]

 [0 -2  0]

 [0  0 -2]
 ? msstar(M) \\ * involution
 %3 =
 [1 0 0]

 [0 0 1]

 [0 1 0]

 ? Mp = msinit(11,2, 1); msdim(Mp) \\ + part
 %4 = 2
 ? mshecke(Mp,2)  \\ T_2 action on M^+
 %5 =
 [3  2]

 [0 -2]
 ? msstar(Mp)
 %6 =
 [1 0]

 [0 1]
 @eprog